Subgroups — #3498×D₆₇ #31764146

Order 17152.

12982 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×H(5,𝔽₂)×D₆₇	C₂	1	2	yes	maximal, complemented
2	#22573987	C₂	1	1	yes	maximal, characteristic, complemented
3	#22573986	C₂	1	4	yes	maximal, complemented
4	#22573985	C₂	1	3	yes	maximal, complemented
5	#22573984	C₂	1	6	yes	maximal, complemented
6	#22573983	C₂	1	2	yes	maximal, complemented
7	#22573982	C₂	1	3	yes	maximal, complemented
8	#22573981	C₂	1	12	yes	maximal, complemented
9	#550×D₆₇	C₂	1	4	yes	maximal, complemented
10	D₄²×D₆₇	C₂	1	12	yes	maximal, complemented
11	#535×D₆₇	C₂	1	6	yes	maximal, complemented
12	#532×D₆₇	C₂	1	3	yes	maximal, complemented
13	C₂×#127×D₆₇	C₂	1	3	yes	maximal, complemented
14	C₄×#41×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14524089	C₂²	1	2	yes	complemented
17	C₂×#14524089	C₂²	1	6	yes	complemented
18	C₂×#14524089	C₂²	1	4	yes	complemented
19	C₂×#14524088	C₂²	1	12	yes	complemented
20	C₂×#14524088	C₂²	1	6	yes	complemented
21	H(5,𝔽₂)×D₆₇	—	2	32	no	—
22	C₂×#41×D₆₇	C₂²	1	1	yes	characteristic
23	C₂×#41×D₆₇	C₂²	1	4	yes	complemented
24	C₂×#41×D₆₇	C₂²	1	6	yes	complemented
25	C₂²×D₄×D₆₇	C₂²	1	12	yes	complemented
26	C₂²×D₄×D₆₇	C₂²	1	6	yes	complemented
27	C₂²×D₄×D₆₇	C₂²	1	12	yes	complemented
28	#16864068	C₂²	1	4	yes	complemented
29	#16864067	C₂²	1	12	yes	complemented
30	#16864066	C₂²	1	12	yes	complemented
31	#16864065	C₂²	1	8	yes	complemented
32	#16864064	C₂²	1	24	yes	complemented
33	D₄×D₂₆₈	C₂²	1	12	yes	complemented
34	D₄×D₂₆₈	C₂²	1	12	yes	complemented
35	#16864031	C₂²	1	12	yes	complemented
36	#16864030	C₂²	1	24	yes	complemented
37	#16864030	C₂²	1	24	yes	complemented
38	D₄×C₂²⋊D₆₇	C₂²	1	24	yes	complemented
39	D₄×C₂²⋊D₆₇	C₂²	1	24	yes	complemented
40	#16864028	C₂²	1	48	yes	complemented
41	#16863965	C₂²	1	6	yes	complemented
42	#16863964	C₂²	1	12	yes	complemented
43	#16863963	C₂²	1	6	yes	complemented
44	#16863962	C₂²	1	24	yes	complemented
45	#16863961	C₂²	1	24	yes	complemented
46	#16863960	C₂²	1	6	yes	complemented
47	#16863959	C₂²	1	12	yes	complemented
48	#16863947	C₂²	1	3	yes	complemented
49	#16863946	C₂²	1	3	yes	complemented
50	#16863945	C₂²	1	6	yes	complemented
51	#16863944	C₂²	1	3	yes	complemented
52	#16863943	C₂²	1	12	yes	complemented
53	#16863942	C₂²	1	6	yes	complemented
54	#16863941	C₂²	1	12	yes	complemented
55	C₄⋊Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂×#14524040	C₂²	1	3	yes	complemented
57	C₂×#14524039	C₂²	1	12	yes	complemented
58	C₂×#14524039	C₂²	1	6	yes	complemented
59	#127×D₆₇	C₂²	1	12	yes	complemented
60	#127×D₆₇	C₂²	1	3	yes	complemented
61	#127×D₆₇	C₂²	1	6	yes	complemented
62	#127×D₆₇	C₂²	1	12	yes	complemented
63	#127×D₆₇	C₂²	1	6	yes	complemented
64	#127×D₆₇	C₂²	1	6	yes	complemented
65	#124×D₆₇	C₂²	1	6	yes	complemented
66	#121×D₆₇	C₂²	1	12	yes	complemented
67	#121×D₆₇	C₂²	1	24	yes	complemented
68	#120×D₆₇	C₂²	1	24	yes	complemented
69	#41×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
70	C₄×#11761629	C₂²	1	2	yes	complemented
71	C₄×#11761628	C₂²	1	3	yes	complemented
72	#16863864	C₂²	1	3	yes	complemented
73	C₄×#11761627	C₂²	1	6	yes	complemented
74	C₄×Q₈×D₆₇	C₂²	1	2	yes	complemented
75	C₄×D₄×D₆₇	C₂²	1	6	yes	complemented
76	C₄×D₄×D₆₇	C₂²	1	12	yes	complemented
77	#117×D₆₇	C₂²	1	3	yes	complemented
78	C₂×C₄²×D₆₇	C₂²	1	3	yes	complemented
79	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	complemented
80	#550×C₆₇	C₂²	1	4	yes	complemented
81	D₄²×C₆₇	C₂²	1	12	yes	complemented
82	#535×C₆₇	C₂²	1	6	yes	complemented
83	#532×C₆₇	C₂²	1	3	yes	complemented
84	C₂×#127×C₆₇	C₂²	1	3	yes	complemented
85	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	C₂⁴×D₆₇	C₂³	1	12	yes	—
87	#14524089	—	2	32	no	—
88	#14524089	—	2	48	no	—
89	#14524089	—	2	16	no	—
90	#14524088	—	2	48	no	—
91	#14524088	—	2	96	no	—
92	C₂×#11761629	C₂³	1	1	yes	characteristic
93	C₂×#11761629	C₂³	1	4	yes	complemented
94	C₂×#11761629	C₂³	1	6	yes	complemented
95	C₂×#11761628	C₂³	1	3	yes	—
96	C₂×#11761628	C₂³	1	12	yes	complemented
97	C₂×#11761628	C₂³	1	6	yes	complemented
98	C₂×#11761628	C₂³	1	12	yes	complemented
99	C₂×#11761627	C₂³	1	3	yes	—
100	C₂×#11761627	C₂³	1	12	yes	complemented
101	C₂×#11761627	C₂³	1	12	yes	complemented
102	C₂×#11761627	C₂³	1	6	yes	complemented
103	#41×D₆₇	—	2	32	no	—
104	#41×D₆₇	—	2	48	no	—
105	#41×D₆₇	D₄	1	16	yes	complemented
106	C₂×Q₈×D₆₇	C₂³	1	2	yes	—
107	C₂×Q₈×D₆₇	C₂³	1	1	yes	characteristic
108	C₂²×D₂₆₈	C₂³	1	12	yes	complemented
109	C₂²×D₂₆₈	C₂³	1	6	yes	complemented
110	C₂²×D₂₆₈	C₂³	1	12	yes	complemented
111	C₂²×C₂²⋊D₆₇	C₂³	1	24	yes	complemented
112	C₂²×C₂²⋊D₆₇	C₂³	1	12	yes	complemented
113	C₂²×C₂²⋊D₆₇	C₂³	1	24	yes	complemented
114	C₂×D₄×D₆₇	—	2	96	no	—
115	C₂×D₄×D₆₇	—	2	48	no	—
116	C₂×D₄×D₆₇	—	4	48	no	—
117	C₂×D₄×D₆₇	C₂³	1	12	yes	—
118	C₂×D₄×D₆₇	C₂³	1	12	yes	—
119	C₂×D₄×D₆₇	C₂³	1	12	yes	—
120	C₂×D₄×D₆₇	C₂³	1	6	yes	—
121	C₂×D₄×D₆₇	C₂³	1	24	yes	—
122	C₂×D₄×D₆₇	C₂³	1	3	yes	—
123	C₂×D₄×D₆₇	C₂³	1	24	yes	complemented
124	C₂×D₄×D₆₇	C₂³	1	12	yes	complemented
125	C₂×D₄×D₆₇	C₂³	1	12	yes	complemented
126	C₂×D₄×D₆₇	C₂³	1	12	yes	complemented
127	C₂×D₄×D₆₇	C₂³	1	12	yes	complemented
128	C₂×D₄×D₆₇	C₂³	1	24	yes	complemented
129	C₂×D₄×D₆₇	C₂³	1	24	yes	complemented
130	C₂²×C₄×D₆₇	C₂³	1	6	yes	—
131	C₂²×C₄×D₆₇	C₂³	1	12	yes	—
132	C₂²×C₄×D₆₇	C₂³	1	3	yes	—
133	#14524043	C₂³	1	1	yes	characteristic, complemented
134	#14524042	C₂³	1	4	yes	complemented
135	#14524041	C₂³	1	2	yes	complemented
136	#14524040	C₂³	1	12	yes	complemented
137	#14524040	C₂³	1	3	yes	complemented
138	#14524040	C₂³	1	6	yes	complemented
139	#14524039	C₂³	1	24	yes	complemented
140	#14524039	C₂³	1	24	yes	complemented
141	#14524039	C₂³	1	24	yes	complemented
142	#14524039	C₂³	1	12	yes	complemented
143	#14524039	C₂³	1	6	yes	complemented
144	#14524039	C₂³	1	12	yes	complemented
145	#14524039	C₂³	1	24	yes	complemented
146	#14524032	C₂³	1	6	yes	complemented
147	#14524031	C₂³	1	6	yes	complemented
148	#14524030	C₂³	1	6	yes	complemented
149	#14524029	C₂³	1	24	yes	complemented
150	#14524018	C₂³	1	12	yes	complemented
151	#14524018	C₂³	1	24	yes	complemented
152	#14524017	C₂³	1	12	yes	complemented
153	#14524017	C₂³	1	24	yes	complemented
154	#14524016	C₂³	1	24	yes	complemented
155	#14524016	C₂³	1	48	yes	complemented
156	#14524015	C₂³	1	24	yes	complemented
157	#14524015	C₂³	1	48	yes	complemented
158	#14524014	C₂³	1	12	yes	complemented
159	#14524014	C₂³	1	24	yes	complemented
160	#14524013	C₂³	1	24	yes	complemented
161	#14524013	C₂³	1	48	yes	complemented
162	#14524012	C₂³	1	24	yes	complemented
163	#14524011	C₂³	1	48	yes	complemented
164	#14524011	C₂³	1	24	yes	complemented
165	Q₈×Dic₆₇	C₂³	1	2	yes	complemented
166	C₄×Dic₁₃₄	C₂³	1	6	yes	complemented
167	#14524008	C₂³	1	6	yes	complemented
168	C₄×D₂₆₈	C₂³	1	6	yes	complemented
169	C₄×D₂₆₈	C₂³	1	12	yes	complemented
170	D₄×Dic₆₇	C₂³	1	6	yes	complemented
171	D₄×Dic₆₇	C₂³	1	12	yes	complemented
172	#14524005	C₂³	1	6	yes	complemented
173	#14524005	C₂³	1	12	yes	complemented
174	C₄×C₂²⋊D₆₇	C₂³	1	12	yes	complemented
175	C₄×C₂²⋊D₆₇	C₂³	1	24	yes	complemented
176	(C₂²⋊D₆₇)⋊C₄	C₂³	1	12	yes	complemented
177	(C₂²⋊D₆₇)⋊C₄	C₂³	1	24	yes	complemented
178	#14524002	C₂³	1	3	yes	complemented
179	#14524001	C₂³	1	6	yes	complemented
180	#14524000	C₂³	1	6	yes	complemented
181	#14523999	C₂³	1	6	yes	complemented
182	C₄⋊C₄×D₆₇	C₂³	1	6	yes	—
183	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
184	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	—
185	C₂²⋊C₄×D₆₇	C₂³	1	24	yes	—
186	C₂×C₄×Dic₆₇	C₂³	1	6	yes	complemented
187	C₂×C₄×Dic₆₇	C₂³	1	3	yes	complemented
188	C₄²×D₆₇	C₂³	1	1	yes	characteristic
189	C₄²×D₆₇	C₂³	1	3	yes	—
190	C₄²×D₆₇	C₂³	1	6	yes	—
191	C₄²×D₆₇	C₂³	1	6	yes	complemented
192	C₄²×D₆₇	C₂³	1	3	yes	complemented
193	C₄²×D₆₇	C₂³	1	3	yes	complemented
194	H(5,𝔽₂)×C₆₇	—	2	16	no	—
195	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×#41×C₆₇	C₂³	1	4	yes	complemented
197	C₂×#41×C₆₇	C₂³	1	6	yes	complemented
198	C₂²×D₄×C₆₇	C₂³	1	12	yes	complemented
199	C₂²×D₄×C₆₇	C₂³	1	6	yes	complemented
200	C₂²×D₄×C₆₇	C₂³	1	12	yes	complemented
201	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
202	#127×C₆₇	C₂³	1	12	yes	complemented
203	#127×C₆₇	C₂³	1	3	yes	complemented
204	#127×C₆₇	C₂³	1	6	yes	complemented
205	#124×C₆₇	C₂³	1	6	yes	complemented
206	#121×C₆₇	C₂³	1	12	yes	complemented
207	#121×C₆₇	C₂³	1	24	yes	complemented
208	#120×C₆₇	C₂³	1	24	yes	complemented
209	C₄×Q₈×C₆₇	C₂³	1	2	yes	complemented
210	C₄×D₄×C₆₇	C₂³	1	6	yes	complemented
211	C₄×D₄×C₆₇	C₂³	1	12	yes	complemented
212	#117×C₆₇	C₂³	1	3	yes	complemented
213	C₂×C₄²×C₆₇	C₂³	1	3	yes	complemented
214	C₂³×D₆₇	—	2	48	no	—
215	C₂³×D₆₇	—	4	48	no	—
216	C₂³×D₆₇	C₂⁴	1	12	yes	—
217	C₂³×D₆₇	C₂⁴	1	3	yes	—
218	C₂³×D₆₇	C₂⁴	1	24	yes	—
219	C₂³×D₆₇	C₂⁴	1	12	yes	—
220	#11761629	—	2	16	no	—
221	#11761629	—	2	24	no	—
222	#11761629	C₂×D₄	1	8	yes	complemented
223	#11761628	—	2	24	no	—
224	#11761628	—	2	48	no	—
225	#11761628	—	2	48	no	—
226	#11761628	C₂×D₄	1	24	yes	complemented
227	#11761627	—	2	48	no	—
228	#11761627	—	2	24	no	—
229	#11761627	—	2	48	no	—
230	#11761627	C₂×D₄	1	24	yes	complemented
231	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
232	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
233	C₂×Dic₁₃₄	C₂⁴	1	3	yes	—
234	Q₈×D₆₇	—	2	8	no	—
235	Q₈×D₆₇	C₂×D₄	1	8	yes	complemented
236	C₂×D₂₆₈	—	2	24	no	—
237	C₂×D₂₆₈	—	2	48	no	—
238	C₂×D₂₆₈	—	4	24	no	—
239	C₂×D₂₆₈	C₂⁴	1	12	yes	—
240	C₂×D₂₆₈	C₂⁴	1	12	yes	—
241	C₂×D₂₆₈	C₂⁴	1	12	yes	—
242	C₂×D₂₆₈	C₂⁴	1	6	yes	—
243	C₂×D₂₆₈	C₂⁴	1	24	yes	—
244	C₂×D₂₆₈	C₂⁴	1	3	yes	—
245	C₂×C₂²⋊D₆₇	—	2	96	no	—
246	C₂×C₂²⋊D₆₇	—	2	48	no	—
247	C₂×C₂²⋊D₆₇	—	4	48	no	—
248	C₂×C₂²⋊D₆₇	C₂⁴	1	24	yes	—
249	C₂×C₂²⋊D₆₇	C₂⁴	1	12	yes	—
250	C₂×C₂²⋊D₆₇	C₂⁴	1	12	yes	—
251	C₂×C₂²⋊D₆₇	C₂⁴	1	24	yes	—
252	C₂×C₂²⋊D₆₇	C₂⁴	1	12	yes	—
253	C₂×C₂²⋊D₆₇	C₂⁴	1	48	yes	—
254	C₂×C₂²⋊D₆₇	C₂⁴	1	6	yes	—
255	D₄×D₆₇	—	2	48	no	—
256	D₄×D₆₇	—	2	48	no	—
257	D₄×D₆₇	—	2	96	no	—
258	D₄×D₆₇	—	2	48	no	—
259	D₄×D₆₇	—	2	48	no	—
260	D₄×D₆₇	—	2	24	no	—
261	D₄×D₆₇	—	2	48	no	—
262	D₄×D₆₇	—	2	48	no	—
263	D₄×D₆₇	—	2	48	no	—
264	D₄×D₆₇	—	4	48	no	—
265	D₄×D₆₇	—	4	48	no	—
266	D₄×D₆₇	—	4	48	no	—
267	D₄×D₆₇	C₂×D₄	1	24	yes	complemented
268	C₂²×Dic₆₇	C₂⁴	1	6	yes	—
269	C₂²×Dic₆₇	C₂⁴	1	12	yes	—
270	C₂²×Dic₆₇	C₂⁴	1	3	yes	—
271	C₂×C₄×D₆₇	—	2	48	no	—
272	C₂×C₄×D₆₇	—	2	24	no	—
273	C₂×C₄×D₆₇	C₂×D₄	1	24	yes	complemented
274	C₂×C₄×D₆₇	C₂⁴	1	6	yes	—
275	C₂×C₄×D₆₇	C₂⁴	1	6	yes	—
276	C₂×C₄×D₆₇	C₂⁴	1	6	yes	—
277	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
278	C₂×C₄×D₆₇	C₂⁴	1	12	yes	—
279	C₂×C₄×D₆₇	C₂⁴	1	12	yes	—
280	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×D₆₇	C₂⁴	1	3	yes	—
282	C₂×C₄×D₆₇	C₂⁴	1	3	yes	—
283	C₂×C₄×D₆₇	C₂⁴	1	3	yes	—
284	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
285	C₄⋊Dic₆₇	C₂⁴	1	6	yes	—
286	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
287	Dic₆₇⋊C₄	C₂⁴	1	12	yes	—
288	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
289	C₂²⋊Dic₆₇	C₂⁴	1	6	yes	—
290	C₂²⋊Dic₆₇	C₂⁴	1	24	yes	—
291	(C₂×D₆₇)⋊C₄	C₂⁴	1	12	yes	—
292	(C₂×D₆₇)⋊C₄	C₂⁴	1	24	yes	—
293	(C₂×D₆₇)⋊C₄	C₂⁴	1	24	yes	—
294	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
295	C₄×Dic₆₇	C₂⁴	1	2	yes	—
296	C₄×Dic₆₇	C₂⁴	1	6	yes	—
297	C₄×Dic₆₇	C₂⁴	1	3	yes	—
298	C₄×Dic₆₇	C₂⁴	1	6	yes	—
299	C₄×Dic₆₇	C₂⁴	1	6	yes	—
300	C₄×Dic₆₇	C₂⁴	1	6	yes	—
301	C₂⁴×C₆₇	C₂⁴	1	12	yes	—
302	#41×C₆₇	—	2	16	no	—
303	#41×C₆₇	—	2	24	no	—
304	#41×C₆₇	C₂×D₄	1	8	yes	complemented
305	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
306	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂×D₄×C₆₇	—	2	48	no	—
308	C₂×D₄×C₆₇	—	2	24	no	—
309	C₂×D₄×C₆₇	—	4	24	no	—
310	C₂×D₄×C₆₇	C₂⁴	1	12	yes	—
311	C₂×D₄×C₆₇	C₂⁴	1	12	yes	—
312	C₂×D₄×C₆₇	C₂⁴	1	12	yes	—
313	C₂×D₄×C₆₇	C₂⁴	1	6	yes	—
314	C₂×D₄×C₆₇	C₂⁴	1	24	yes	—
315	C₂×D₄×C₆₇	C₂⁴	1	3	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
317	C₂²×C₄×C₆₇	C₂⁴	1	12	yes	—
318	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
319	C₄⋊C₄×C₆₇	C₂⁴	1	6	yes	—
320	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
321	C₂²⋊C₄×C₆₇	C₂⁴	1	6	yes	—
322	C₂²⋊C₄×C₆₇	C₂⁴	1	24	yes	—
323	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₄²×C₆₇	C₂⁴	1	3	yes	—
325	C₄²×C₆₇	C₂⁴	1	6	yes	—
326	C₂³×C₆₇	—	2	24	no	—
327	C₂³×C₆₇	—	4	24	no	—
328	C₂³×C₆₇	C₂⁵	1	12	yes	—
329	C₂³×C₆₇	C₂⁵	1	3	yes	—
330	C₂²×D₆₇	—	2	12	no	—
331	C₂²×D₆₇	—	2	24	no	—
332	C₂²×D₆₇	—	2	24	no	—
333	C₂²×D₆₇	—	2	48	no	—
334	C₂²×D₆₇	—	2	48	no	—
335	C₂²×D₆₇	—	4	48	no	—
336	C₂²×D₆₇	—	4	24	no	—
337	C₂²×D₆₇	—	8	96	no	—
338	C₂²×D₆₇	C₂²×D₄	1	12	yes	—
339	C₂²×D₆₇	C₂⁵	1	12	yes	—
340	C₂²×D₆₇	C₂⁵	1	3	yes	—
341	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
342	Q₈×C₆₇	—	2	4	no	—
343	Q₈×C₆₇	C₂²×D₄	1	4	yes	complemented
344	D₄×C₆₇	—	2	24	no	—
345	D₄×C₆₇	—	2	12	no	—
346	D₄×C₆₇	—	2	24	no	—
347	D₄×C₆₇	—	2	24	no	—
348	D₄×C₆₇	—	4	24	no	—
349	D₄×C₆₇	C₂²×D₄	1	12	yes	complemented
350	C₂×C₄×C₆₇	—	2	24	no	—
351	C₂×C₄×C₆₇	—	2	12	no	—
352	C₂×C₄×C₆₇	C₂²×D₄	1	12	yes	complemented
353	C₂×C₄×C₆₇	C₂⁵	1	6	yes	—
354	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
355	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
356	C₂×C₄×C₆₇	C₂⁵	1	3	yes	—
357	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
358	C₂²⋊D₆₇	—	2	24	no	—
359	C₂²⋊D₆₇	—	2	24	no	—
360	C₂²⋊D₆₇	—	2	24	no	—
361	C₂²⋊D₆₇	—	2	48	no	—
362	C₂²⋊D₆₇	—	2	48	no	—
363	C₂²⋊D₆₇	—	4	48	no	—
364	C₂²⋊D₆₇	C₂²×D₄	1	24	yes	complemented
365	C₂×Dic₆₇	—	2	24	no	—
366	C₂×Dic₆₇	—	2	12	no	—
367	C₂×Dic₆₇	C₂²×D₄	1	12	yes	complemented
368	C₂×Dic₆₇	C₂⁵	1	6	yes	—
369	C₂×Dic₆₇	C₂⁵	1	4	yes	—
370	C₂×Dic₆₇	C₂⁵	1	1	yes	characteristic
371	C₂×Dic₆₇	C₂⁵	1	3	yes	—
372	C₂×Dic₆₇	C₂⁵	1	2	yes	—
373	D₂₆₈	—	2	24	no	—
374	D₂₆₈	—	2	12	no	—
375	D₂₆₈	—	2	24	no	—
376	D₂₆₈	—	2	24	no	—
377	D₂₆₈	—	4	24	no	—
378	D₂₆₈	C₂²×D₄	1	12	yes	complemented
379	C₄×D₆₇	—	2	8	no	—
380	C₄×D₆₇	—	2	12	no	—
381	C₄×D₆₇	—	2	24	no	—
382	C₄×D₆₇	—	2	12	no	—
383	C₄×D₆₇	—	2	24	no	—
384	C₄×D₆₇	—	2	12	no	—
385	C₄×D₆₇	C₂²×D₄	1	12	yes	—
386	C₄×D₆₇	C₂²×D₄	1	4	yes	—
387	C₄×D₆₇	C₂²×D₄	1	12	yes	complemented
388	C₄×D₆₇	C₂²×D₄	1	12	yes	complemented
389	C₄×D₆₇	H(5,𝔽₂)	1	8	yes	complemented
390	Dic₁₃₄	—	2	4	no	—
391	Dic₁₃₄	—	2	8	no	—
392	Dic₁₃₄	C₂²×D₄	1	12	yes	complemented
393	C₂²×C₆₇	—	2	6	no	—
394	C₂²×C₆₇	—	2	12	no	—
395	C₂²×C₆₇	—	2	24	no	—
396	C₂²×C₆₇	—	8	24	no	—
397	C₂²×C₆₇	C₂³×D₄	1	6	yes	—
398	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
399	C₂×D₆₇	—	2	6	no	—
400	C₂×D₆₇	—	2	24	no	—
401	C₂×D₆₇	—	2	12	no	—
402	C₂×D₆₇	—	2	24	no	—
403	C₂×D₆₇	—	4	48	no	—
404	C₂×D₆₇	—	8	48	no	—
405	C₂×D₆₇	—	8	24	no	—
406	C₂×D₆₇	C₂³×D₄	1	6	yes	—
407	C₂×D₆₇	C₂³×D₄	1	2	yes	—
408	C₂×D₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
409	C₄×C₆₇	—	2	4	no	—
410	C₄×C₆₇	—	2	6	no	—
411	C₄×C₆₇	C₂³×D₄	1	2	yes	—
412	C₄×C₆₇	C₂³×D₄	1	6	yes	—
413	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	complemented
414	Dic₆₇	—	2	4	no	—
415	Dic₆₇	—	2	6	no	—
416	Dic₆₇	C₂³×D₄	1	2	yes	—
417	Dic₆₇	C₂³×D₄	1	6	yes	—
418	Dic₆₇	C₂×H(5,𝔽₂)	1	4	yes	complemented
419	C₂×#3498	—	67	1	no	maximal, Sylow
420	C₂×C₆₇	—	2	6	no	—
421	C₂×C₆₇	—	4	12	no	—
422	C₂×C₆₇	C₂⁴×D₄	1	1	yes	characteristic
423	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	2	yes	—
424	D₆₇	—	2	6	no	—
425	D₆₇	—	4	12	no	—
426	D₆₇	#3498	1	4	yes	direct product factor
427	C₂²×H(5,𝔽₂)	—	67	2	no	—
428	#3498	—	67	2	no	—
429	#3498	—	67	4	no	—
430	#3498	—	67	12	no	—
431	#3498	—	67	6	no	—
432	#3498	—	67	3	no	—
433	#3498	—	67	3	no	—
434	#3498	—	67	1	no	—
435	#3498	D₆₇	1	1	yes	characteristic, direct product factor
436	C₂×#550	—	67	4	no	—
437	C₂×D₄²	—	67	12	no	—
438	C₂×#535	—	67	6	no	—
439	C₂×#532	—	67	3	no	—
440	C₂²×#127	—	67	3	no	—
441	C₂×C₄×#41	—	67	1	no	—
442	C₆₇	C₂×#3498	1	1	yes	characteristic, complemented, Sylow
443	C₂×H(5,𝔽₂)	—	67	2	no	—
444	C₂×H(5,𝔽₂)	—	67	4	no	—
445	C₂×H(5,𝔽₂)	—	67	6	no	—
446	C₂×H(5,𝔽₂)	—	67	12	no	—
447	C₂×H(5,𝔽₂)	—	67	6	no	—
448	C₂×H(5,𝔽₂)	—	134	32	no	—
449	C₂×H(5,𝔽₂)	C₂×D₆₇	1	2	yes	complemented
450	C₂²×#41	—	67	1	no	—
451	C₂²×#41	—	67	6	no	—
452	C₂²×#41	—	67	4	no	—
453	C₂³×D₄	—	67	12	no	—
454	C₂³×D₄	—	67	6	no	—
455	C₂³×D₄	—	67	12	no	—
456	#550	—	67	8	no	—
457	#550	—	67	12	no	—
458	#550	—	67	24	no	—
459	#550	—	67	4	no	—
460	#550	—	67	12	no	—
461	#550	C₂×D₆₇	1	4	yes	complemented
462	D₄²	—	67	24	no	—
463	D₄²	—	67	24	no	—
464	D₄²	—	67	12	no	—
465	D₄²	—	67	24	no	—
466	D₄²	—	67	24	no	—
467	D₄²	—	67	48	no	—
468	D₄²	—	67	12	no	—
469	D₄²	—	67	12	no	—
470	D₄²	C₂×D₆₇	1	12	yes	complemented
471	#535	—	67	6	no	—
472	#535	—	67	6	no	—
473	#535	—	67	12	no	—
474	#535	—	67	12	no	—
475	#535	—	67	24	no	—
476	#535	—	67	24	no	—
477	#535	—	67	6	no	—
478	#535	C₂×D₆₇	1	6	yes	complemented
479	#532	—	67	6	no	—
480	#532	—	67	3	no	—
481	#532	—	67	3	no	—
482	#532	—	67	6	no	—
483	#532	—	67	12	no	—
484	#532	—	67	12	no	—
485	#532	—	67	3	no	—
486	#532	C₂×D₆₇	1	3	yes	complemented
487	C₂×C₄⋊Q₈	—	67	1	no	—
488	C₂×#127	—	67	6	no	—
489	C₂×#127	—	67	12	no	—
490	C₂×#127	—	67	3	no	—
491	C₂×#127	—	67	6	no	—
492	C₂×#127	—	67	12	no	—
493	C₂×#127	—	67	12	no	—
494	C₂×#127	—	67	6	no	—
495	C₂×#127	—	67	6	no	—
496	C₂×#127	—	67	3	no	—
497	C₂×#127	C₂×D₆₇	1	3	yes	complemented
498	C₂×#124	—	67	6	no	—
499	C₂×#121	—	67	12	no	—
500	C₂×#121	—	67	24	no	—
501	C₂×#120	—	67	24	no	—
502	C₄×#41	—	67	1	no	—
503	C₄×#41	—	67	2	no	—
504	C₄×#41	—	67	6	no	—
505	C₄×#41	—	67	3	no	—
506	C₄×#41	—	67	3	no	—
507	C₄×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
508	C₂×C₄×Q₈	—	67	2	no	—
509	C₂×C₄×D₄	—	67	6	no	—
510	C₂×C₄×D₄	—	67	12	no	—
511	C₂×#117	—	67	3	no	—
512	C₂²×C₄²	—	67	3	no	—
513	C₂⁵	—	67	12	no	—
514	H(5,𝔽₂)	—	2	16	no	—
515	H(5,𝔽₂)	—	134	96	no	—
516	H(5,𝔽₂)	—	134	48	no	—
517	H(5,𝔽₂)	—	134	32	no	—
518	H(5,𝔽₂)	—	134	48	no	—
519	H(5,𝔽₂)	—	134	16	no	—
520	C₂×#41	—	67	16	no	—
521	C₂×#41	—	67	1	no	—
522	C₂×#41	—	67	6	no	—
523	C₂×#41	—	67	4	no	—
524	C₂×#41	—	67	3	no	—
525	C₂×#41	—	67	12	no	—
526	C₂×#41	—	67	6	no	—
527	C₂×#41	—	67	12	no	—
528	C₂×#41	—	67	3	no	—
529	C₂×#41	—	67	12	no	—
530	C₂×#41	—	67	6	no	—
531	C₂×#41	—	67	12	no	—
532	C₂×#41	—	134	48	no	—
533	C₂×#41	—	134	32	no	—
534	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
535	C₂×#41	C₂²×D₆₇	1	6	yes	complemented
536	C₂×#41	C₂²×D₆₇	1	4	yes	complemented
537	C₂²×Q₈	—	67	1	no	—
538	C₂²×Q₈	—	67	2	no	—
539	C₂²×D₄	—	268	48	no	—
540	C₂²×D₄	—	67	24	no	—
541	C₂²×D₄	—	67	24	no	—
542	C₂²×D₄	—	67	24	no	—
543	C₂²×D₄	—	67	24	no	—
544	C₂²×D₄	—	67	3	no	—
545	C₂²×D₄	—	67	12	no	—
546	C₂²×D₄	—	67	24	no	—
547	C₂²×D₄	—	67	12	no	—
548	C₂²×D₄	—	67	12	no	—
549	C₂²×D₄	—	67	12	no	—
550	C₂²×D₄	—	67	6	no	—
551	C₂²×D₄	—	67	12	no	—
552	C₂²×D₄	—	67	12	no	—
553	C₂²×D₄	—	67	24	no	—
554	C₂²×D₄	—	67	12	no	—
555	C₂²×D₄	—	67	12	no	—
556	C₂²×D₄	—	67	12	no	—
557	C₂²×D₄	—	67	6	no	—
558	C₂²×D₄	—	67	12	no	—
559	C₂²×D₄	—	134	48	no	—
560	C₂²×D₄	—	134	96	no	—
561	C₂²×D₄	C₂²×D₆₇	1	6	yes	complemented
562	C₂²×D₄	C₂²×D₆₇	1	12	yes	complemented
563	C₂²×D₄	C₂²×D₆₇	1	12	yes	complemented
564	C₂³×C₄	—	67	3	no	—
565	C₂³×C₄	—	67	6	no	—
566	C₂³×C₄	—	67	12	no	—
567	C₄⋊Q₈	—	67	2	no	—
568	C₄⋊Q₈	—	67	4	no	—
569	C₄⋊Q₈	—	67	1	no	—
570	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic, complemented
571	#127	—	67	6	no	—
572	#127	—	67	12	no	—
573	#127	—	67	12	no	—
574	#127	—	67	24	no	—
575	#127	—	67	24	no	—
576	#127	—	67	24	no	—
577	#127	—	67	24	no	—
578	#127	—	67	3	no	—
579	#127	—	67	6	no	—
580	#127	—	67	12	no	—
581	#127	C₂²×D₆₇	1	3	yes	complemented
582	#127	C₂²×D₆₇	1	6	yes	complemented
583	#127	C₂²×D₆₇	1	12	yes	complemented
584	#124	—	67	6	no	—
585	#124	—	67	6	no	—
586	#124	—	67	24	no	—
587	#124	—	67	6	no	—
588	#124	C₂²×D₆₇	1	6	yes	complemented
589	#121	—	67	12	no	—
590	#121	—	67	24	no	—
591	#121	—	67	24	no	—
592	#121	—	67	48	no	—
593	#121	—	67	12	no	—
594	#121	—	67	24	no	—
595	#121	—	67	12	no	—
596	#121	—	67	24	no	—
597	#121	—	67	24	no	—
598	#121	—	67	48	no	—
599	#121	C₂²×D₆₇	1	12	yes	complemented
600	#121	C₂²×D₆₇	1	24	yes	complemented
601	#120	—	67	24	no	—
602	#120	—	67	24	no	—
603	#120	—	67	48	no	—
604	#120	—	67	48	no	—
605	#120	—	67	24	no	—
606	#120	C₂²×D₆₇	1	24	yes	complemented
607	C₄×Q₈	—	67	2	no	—
608	C₄×Q₈	—	67	6	no	—
609	C₄×Q₈	—	67	6	no	—
610	C₄×Q₈	C₂²×D₆₇	1	2	yes	complemented
611	C₄×D₄	—	67	6	no	—
612	C₄×D₄	—	67	12	no	—
613	C₄×D₄	—	67	12	no	—
614	C₄×D₄	—	67	24	no	—
615	C₄×D₄	—	67	6	no	—
616	C₄×D₄	—	67	12	no	—
617	C₄×D₄	—	67	12	no	—
618	C₄×D₄	—	67	24	no	—
619	C₄×D₄	—	67	6	no	—
620	C₄×D₄	—	67	12	no	—
621	C₄×D₄	C₂²×D₆₇	1	6	yes	complemented
622	C₄×D₄	C₂²×D₆₇	1	12	yes	complemented
623	#117	—	67	3	no	—
624	#117	—	67	6	no	—
625	#117	—	67	6	no	—
626	#117	—	67	6	no	—
627	#117	C₂²×D₆₇	1	3	yes	complemented
628	C₂×C₄⋊C₄	—	67	6	no	—
629	C₂×C₄⋊C₄	—	67	4	no	—
630	C₂×C₂²⋊C₄	—	67	6	no	—
631	C₂×C₂²⋊C₄	—	67	24	no	—
632	C₂×C₄²	—	67	6	no	—
633	C₂×C₄²	—	67	3	no	—
634	C₂×C₄²	—	67	3	no	—
635	C₂×C₄²	—	67	6	no	—
636	C₂×C₄²	—	67	6	no	—
637	C₂×C₄²	—	67	3	no	—
638	C₂×C₄²	—	67	3	no	—
639	C₂×C₄²	—	67	1	no	—
640	C₂×C₄²	C₂²×D₆₇	1	3	yes	complemented
641	C₂⁴	—	268	48	no	—
642	C₂⁴	—	67	24	no	—
643	C₂⁴	—	67	12	no	—
644	C₂⁴	—	67	3	no	—
645	C₂⁴	—	67	12	no	—
646	C₂⁴	—	134	48	no	—
647	C₂⁴	C₂³×D₆₇	1	12	yes	—
648	#41	—	2	16	no	—
649	#41	—	2	24	no	—
650	#41	—	67	8	no	—
651	#41	—	67	24	no	—
652	#41	—	67	24	no	—
653	#41	—	134	48	no	—
654	#41	—	134	48	no	—
655	#41	—	134	48	no	—
656	#41	—	134	24	no	—
657	#41	—	134	24	no	—
658	#41	—	134	48	no	—
659	#41	—	134	16	no	—
660	#41	—	134	24	no	—
661	#41	D₄×D₆₇	1	8	yes	complemented
662	C₂×Q₈	—	67	8	no	—
663	C₂×Q₈	—	67	3	no	—
664	C₂×Q₈	—	67	4	no	—
665	C₂×Q₈	—	67	2	no	—
666	C₂×Q₈	—	134	8	no	—
667	C₂×Q₈	C₂³×D₆₇	1	2	yes	—
668	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
669	C₂×D₄	—	2	48	no	—
670	C₂×D₄	—	2	24	no	—
671	C₂×D₄	—	4	24	no	—
672	C₂×D₄	—	268	24	no	—
673	C₂×D₄	—	268	48	no	—
674	C₂×D₄	—	268	48	no	—
675	C₂×D₄	—	268	48	no	—
676	C₂×D₄	—	268	48	no	—
677	C₂×D₄	—	67	48	no	—
678	C₂×D₄	—	67	6	no	—
679	C₂×D₄	—	67	24	no	—
680	C₂×D₄	—	67	24	no	—
681	C₂×D₄	—	67	12	no	—
682	C₂×D₄	—	67	12	no	—
683	C₂×D₄	—	67	24	no	—
684	C₂×D₄	—	67	12	no	—
685	C₂×D₄	—	67	24	no	—
686	C₂×D₄	—	67	3	no	—
687	C₂×D₄	—	67	12	no	—
688	C₂×D₄	—	67	12	no	—
689	C₂×D₄	—	67	12	no	—
690	C₂×D₄	—	67	6	no	—
691	C₂×D₄	—	134	48	no	—
692	C₂×D₄	—	134	48	no	—
693	C₂×D₄	—	134	24	no	—
694	C₂×D₄	—	134	48	no	—
695	C₂×D₄	—	134	48	no	—
696	C₂×D₄	—	134	48	no	—
697	C₂×D₄	—	134	48	no	—
698	C₂×D₄	—	134	96	no	—
699	C₂×D₄	—	134	48	no	—
700	C₂×D₄	—	134	48	no	—
701	C₂×D₄	—	134	96	no	—
702	C₂×D₄	—	134	48	no	—
703	C₂×D₄	—	134	24	no	—
704	C₂×D₄	C₂³×D₆₇	1	12	yes	—
705	C₂×D₄	C₂³×D₆₇	1	12	yes	—
706	C₂×D₄	C₂³×D₆₇	1	12	yes	—
707	C₂×D₄	C₂³×D₆₇	1	6	yes	—
708	C₂×D₄	C₂³×D₆₇	1	24	yes	—
709	C₂×D₄	C₂³×D₆₇	1	3	yes	—
710	C₂²×C₄	—	67	3	no	—
711	C₂²×C₄	—	67	24	no	—
712	C₂²×C₄	—	67	2	no	—
713	C₂²×C₄	—	67	1	no	—
714	C₂²×C₄	—	67	3	no	—
715	C₂²×C₄	—	67	3	no	—
716	C₂²×C₄	—	67	3	no	—
717	C₂²×C₄	—	67	6	no	—
718	C₂²×C₄	—	67	12	no	—
719	C₂²×C₄	—	67	6	no	—
720	C₂²×C₄	—	67	6	no	—
721	C₂²×C₄	—	67	6	no	—
722	C₂²×C₄	—	67	4	no	—
723	C₂²×C₄	—	67	12	no	—
724	C₂²×C₄	—	67	12	no	—
725	C₂²×C₄	—	134	24	no	—
726	C₂²×C₄	—	134	48	no	—
727	C₂²×C₄	C₂³×D₆₇	1	6	yes	—
728	C₂²×C₄	C₂³×D₆₇	1	12	yes	—
729	C₂²×C₄	C₂³×D₆₇	1	3	yes	—
730	C₄⋊C₄	—	67	12	no	—
731	C₄⋊C₄	—	67	6	no	—
732	C₄⋊C₄	—	67	8	no	—
733	C₄⋊C₄	—	67	4	no	—
734	C₄⋊C₄	C₂³×D₆₇	1	6	yes	—
735	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
736	C₂²⋊C₄	—	67	6	no	—
737	C₂²⋊C₄	—	67	24	no	—
738	C₂²⋊C₄	—	67	12	no	—
739	C₂²⋊C₄	—	67	24	no	—
740	C₂²⋊C₄	—	67	24	no	—
741	C₂²⋊C₄	C₂³×D₆₇	1	6	yes	—
742	C₂²⋊C₄	C₂³×D₆₇	1	24	yes	—
743	C₄²	—	67	1	no	—
744	C₄²	—	67	2	no	—
745	C₄²	—	67	6	no	—
746	C₄²	—	67	3	no	—
747	C₄²	—	67	6	no	—
748	C₄²	—	67	6	no	—
749	C₄²	—	67	6	no	—
750	C₄²	C₂³×D₆₇	1	1	yes	characteristic
751	C₄²	C₂³×D₆₇	1	3	yes	—
752	C₄²	C₂³×D₆₇	1	6	yes	—
753	C₂³	—	2	24	no	—
754	C₂³	—	4	24	no	—
755	C₂³	—	268	24	no	—
756	C₂³	—	268	48	no	—
757	C₂³	—	536	96	no	—
758	C₂³	—	67	1	no	—
759	C₂³	—	67	12	no	—
760	C₂³	—	67	3	no	—
761	C₂³	—	67	12	no	—
762	C₂³	—	134	24	no	—
763	C₂³	—	134	48	no	—
764	C₂³	—	134	48	no	—
765	C₂³	—	134	12	no	—
766	C₂³	—	134	24	no	—
767	C₂³	C₂⁴×D₆₇	1	12	yes	—
768	C₂³	C₂⁴×D₆₇	1	3	yes	—
769	Q₈	—	2	4	no	—
770	Q₈	—	67	12	no	—
771	Q₈	—	134	8	no	—
772	Q₈	—	134	4	no	—
773	Q₈	C₂×D₄×D₆₇	1	4	yes	complemented
774	D₄	—	2	24	no	—
775	D₄	—	2	24	no	—
776	D₄	—	2	12	no	—
777	D₄	—	2	24	no	—
778	D₄	—	4	24	no	—
779	D₄	—	268	24	no	—
780	D₄	—	268	48	no	—
781	D₄	—	67	24	no	—
782	D₄	—	67	12	no	—
783	D₄	—	134	24	no	—
784	D₄	—	134	48	no	—
785	D₄	—	134	24	no	—
786	D₄	—	134	48	no	—
787	D₄	—	134	24	no	—
788	D₄	—	134	24	no	—
789	D₄	—	134	24	no	—
790	D₄	—	134	12	no	—
791	D₄	—	134	24	no	—
792	D₄	C₂×D₄×D₆₇	1	12	yes	complemented
793	C₂×C₄	—	2	24	no	—
794	C₂×C₄	—	2	12	no	—
795	C₂×C₄	—	67	12	no	—
796	C₂×C₄	—	67	2	no	—
797	C₂×C₄	—	67	1	no	—
798	C₂×C₄	—	67	3	no	—
799	C₂×C₄	—	67	4	no	—
800	C₂×C₄	—	67	12	no	—
801	C₂×C₄	—	67	12	no	—
802	C₂×C₄	—	67	12	no	—
803	C₂×C₄	—	67	8	no	—
804	C₂×C₄	—	67	6	no	—
805	C₂×C₄	—	67	4	no	—
806	C₂×C₄	—	134	12	no	—
807	C₂×C₄	—	134	24	no	—
808	C₂×C₄	—	134	8	no	—
809	C₂×C₄	—	134	12	no	—
810	C₂×C₄	—	134	12	no	—
811	C₂×C₄	—	134	24	no	—
812	C₂×C₄	—	134	24	no	—
813	C₂×C₄	—	134	12	no	—
814	C₂×C₄	C₂×D₄×D₆₇	1	12	yes	complemented
815	C₂×C₄	C₂⁴×D₆₇	1	6	yes	—
816	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
817	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
818	C₂×C₄	C₂⁴×D₆₇	1	3	yes	—
819	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
820	C₂²	—	2	6	no	—
821	C₂²	—	2	12	no	—
822	C₂²	—	2	24	no	—
823	C₂²	—	8	24	no	—
824	C₂²	—	268	48	no	—
825	C₂²	—	536	24	no	—
826	C₂²	—	536	48	no	—
827	C₂²	—	67	2	no	—
828	C₂²	—	67	4	no	—
829	C₂²	—	67	6	no	—
830	C₂²	—	134	24	no	—
831	C₂²	—	134	12	no	—
832	C₂²	—	134	24	no	—
833	C₂²	—	134	6	no	—
834	C₂²	C₂²×D₄×D₆₇	1	6	yes	—
835	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
836	C₄	—	2	4	no	—
837	C₄	—	2	6	no	—
838	C₄	—	67	2	no	—
839	C₄	—	67	6	no	—
840	C₄	—	67	4	no	—
841	C₄	—	134	4	no	—
842	C₄	—	134	6	no	—
843	C₄	C₂²×D₄×D₆₇	1	6	yes	—
844	C₄	C₂²×D₄×D₆₇	1	2	yes	—
845	C₄	H(5,𝔽₂)×D₆₇	1	4	yes	complemented
846	C₂	—	2	6	no	—
847	C₂	—	4	12	no	—
848	C₂	—	268	12	no	—
849	C₂	—	67	4	no	—
850	C₂	—	134	6	no	—
851	C₂	C₂³×D₄×D₆₇	1	1	yes	characteristic
852	C₂	C₂×H(5,𝔽₂)×D₆₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₆₇
commutator, socle, cosocle	C₂²×C₆₇	C₂⁶
Fitting	C₆₇×#3498	C₂
hypercenter	#3498	D₆₇
hypocenter	C₆₇	C₂×#3498
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #3498

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×H(5,𝔽₂)×D₆₇	C₂	semidirect
2. #22573987	C₂	semidirect
3. #22573986	C₂	semidirect
4. #22573985	C₂	semidirect
5. #22573984	C₂	semidirect
6. #22573983	C₂	semidirect
7. #22573982	C₂	semidirect
8. #22573981	C₂	semidirect
9. #550×D₆₇	C₂	semidirect
10. D₄²×D₆₇	C₂	semidirect
11. #535×D₆₇	C₂	semidirect
12. #532×D₆₇	C₂	semidirect
13. C₂×#127×D₆₇	C₂	semidirect
14. C₄×#41×D₆₇	C₂	semidirect
15. C₆₇×#3498	C₂	semidirect
16. C₂×#14524089	C₂²	semidirect
17. C₂×#14524089	C₂²	semidirect
18. C₂×#14524089	C₂²	semidirect
19. C₂×#14524088	C₂²	semidirect
20. C₂×#14524088	C₂²	semidirect
23. C₂×#41×D₆₇	C₂²	semidirect
24. C₂×#41×D₆₇	C₂²	semidirect
25. C₂²×D₄×D₆₇	C₂²	semidirect
26. C₂²×D₄×D₆₇	C₂²	semidirect
27. C₂²×D₄×D₆₇	C₂²	semidirect
28. #16864068	C₂²	semidirect
29. #16864067	C₂²	semidirect
30. #16864066	C₂²	semidirect
31. #16864065	C₂²	semidirect
32. #16864064	C₂²	semidirect
33. D₄×D₂₆₈	C₂²	semidirect
34. D₄×D₂₆₈	C₂²	semidirect
35. #16864031	C₂²	semidirect
36. #16864030	C₂²	semidirect
37. #16864030	C₂²	semidirect
38. D₄×C₂²⋊D₆₇	C₂²	semidirect
39. D₄×C₂²⋊D₆₇	C₂²	semidirect
40. #16864028	C₂²	semidirect
41. #16863965	C₂²	semidirect
42. #16863964	C₂²	semidirect
43. #16863963	C₂²	semidirect
44. #16863962	C₂²	semidirect
45. #16863961	C₂²	semidirect
46. #16863960	C₂²	semidirect
47. #16863959	C₂²	semidirect
48. #16863947	C₂²	semidirect
49. #16863946	C₂²	semidirect
50. #16863945	C₂²	semidirect
51. #16863944	C₂²	semidirect
52. #16863943	C₂²	semidirect
53. #16863942	C₂²	semidirect
54. #16863941	C₂²	semidirect
55. C₄⋊Q₈×D₆₇	C₂²	semidirect
56. C₂×#14524040	C₂²	semidirect
57. C₂×#14524039	C₂²	semidirect
58. C₂×#14524039	C₂²	semidirect
59. #127×D₆₇	C₂²	semidirect
60. #127×D₆₇	C₂²	semidirect
61. #127×D₆₇	C₂²	semidirect
62. #127×D₆₇	C₂²	semidirect
63. #127×D₆₇	C₂²	semidirect
64. #127×D₆₇	C₂²	semidirect
65. #124×D₆₇	C₂²	semidirect
66. #121×D₆₇	C₂²	semidirect
67. #121×D₆₇	C₂²	semidirect
68. #120×D₆₇	C₂²	semidirect
69. #41×Dic₆₇	C₂²	semidirect
70. C₄×#11761629	C₂²	semidirect
71. C₄×#11761628	C₂²	semidirect
72. #16863864	C₂²	semidirect
73. C₄×#11761627	C₂²	semidirect
74. C₄×Q₈×D₆₇	C₂²	semidirect
75. C₄×D₄×D₆₇	C₂²	semidirect
76. C₄×D₄×D₆₇	C₂²	semidirect
77. #117×D₆₇	C₂²	semidirect
78. C₂×C₄²×D₆₇	C₂²	semidirect
79. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
80. #550×C₆₇	C₂²	semidirect
81. D₄²×C₆₇	C₂²	semidirect
82. #535×C₆₇	C₂²	semidirect
83. #532×C₆₇	C₂²	semidirect
84. C₂×#127×C₆₇	C₂²	semidirect
85. C₄×#41×C₆₇	C₂²	semidirect
93. C₂×#11761629	C₂³	semidirect
94. C₂×#11761629	C₂³	semidirect
96. C₂×#11761628	C₂³	semidirect
97. C₂×#11761628	C₂³	semidirect
98. C₂×#11761628	C₂³	semidirect
100. C₂×#11761627	C₂³	semidirect
101. C₂×#11761627	C₂³	semidirect
102. C₂×#11761627	C₂³	semidirect
105. #41×D₆₇	D₄	semidirect
108. C₂²×D₂₆₈	C₂³	semidirect
109. C₂²×D₂₆₈	C₂³	semidirect
110. C₂²×D₂₆₈	C₂³	semidirect
111. C₂²×C₂²⋊D₆₇	C₂³	semidirect
112. C₂²×C₂²⋊D₆₇	C₂³	semidirect
113. C₂²×C₂²⋊D₆₇	C₂³	semidirect
123. C₂×D₄×D₆₇	C₂³	semidirect
124. C₂×D₄×D₆₇	C₂³	semidirect
125. C₂×D₄×D₆₇	C₂³	semidirect
126. C₂×D₄×D₆₇	C₂³	semidirect
127. C₂×D₄×D₆₇	C₂³	semidirect
128. C₂×D₄×D₆₇	C₂³	semidirect
129. C₂×D₄×D₆₇	C₂³	semidirect
133. #14524043	C₂³	semidirect
134. #14524042	C₂³	semidirect
135. #14524041	C₂³	semidirect
136. #14524040	C₂³	semidirect
137. #14524040	C₂³	semidirect
138. #14524040	C₂³	semidirect
139. #14524039	C₂³	semidirect
140. #14524039	C₂³	semidirect
141. #14524039	C₂³	semidirect
142. #14524039	C₂³	semidirect
143. #14524039	C₂³	semidirect
144. #14524039	C₂³	semidirect
145. #14524039	C₂³	semidirect
146. #14524032	C₂³	semidirect
147. #14524031	C₂³	semidirect
148. #14524030	C₂³	semidirect
149. #14524029	C₂³	semidirect
150. #14524018	C₂³	semidirect
151. #14524018	C₂³	semidirect
152. #14524017	C₂³	semidirect
153. #14524017	C₂³	semidirect
154. #14524016	C₂³	semidirect
155. #14524016	C₂³	semidirect
156. #14524015	C₂³	semidirect
157. #14524015	C₂³	semidirect
158. #14524014	C₂³	semidirect
159. #14524014	C₂³	semidirect
160. #14524013	C₂³	semidirect
161. #14524013	C₂³	semidirect
162. #14524012	C₂³	semidirect
163. #14524011	C₂³	semidirect
164. #14524011	C₂³	semidirect
165. Q₈×Dic₆₇	C₂³	semidirect
166. C₄×Dic₁₃₄	C₂³	semidirect
167. #14524008	C₂³	semidirect
168. C₄×D₂₆₈	C₂³	semidirect
169. C₄×D₂₆₈	C₂³	semidirect
170. D₄×Dic₆₇	C₂³	semidirect
171. D₄×Dic₆₇	C₂³	semidirect
172. #14524005	C₂³	semidirect
173. #14524005	C₂³	semidirect
174. C₄×C₂²⋊D₆₇	C₂³	semidirect
175. C₄×C₂²⋊D₆₇	C₂³	semidirect
176. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
177. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
178. #14524002	C₂³	semidirect
179. #14524001	C₂³	semidirect
180. #14524000	C₂³	semidirect
181. #14523999	C₂³	semidirect
186. C₂×C₄×Dic₆₇	C₂³	semidirect
187. C₂×C₄×Dic₆₇	C₂³	semidirect
191. C₄²×D₆₇	C₂³	semidirect
192. C₄²×D₆₇	C₂³	semidirect
193. C₄²×D₆₇	C₂³	semidirect
196. C₂×#41×C₆₇	C₂³	semidirect
197. C₂×#41×C₆₇	C₂³	semidirect
198. C₂²×D₄×C₆₇	C₂³	semidirect
199. C₂²×D₄×C₆₇	C₂³	semidirect
200. C₂²×D₄×C₆₇	C₂³	semidirect
201. C₄⋊Q₈×C₆₇	C₂³	semidirect
202. #127×C₆₇	C₂³	semidirect
203. #127×C₆₇	C₂³	semidirect
204. #127×C₆₇	C₂³	semidirect
205. #124×C₆₇	C₂³	semidirect
206. #121×C₆₇	C₂³	semidirect
207. #121×C₆₇	C₂³	semidirect
208. #120×C₆₇	C₂³	semidirect
209. C₄×Q₈×C₆₇	C₂³	semidirect
210. C₄×D₄×C₆₇	C₂³	semidirect
211. C₄×D₄×C₆₇	C₂³	semidirect
212. #117×C₆₇	C₂³	semidirect
213. C₂×C₄²×C₆₇	C₂³	semidirect
222. #11761629	C₂×D₄	semidirect
226. #11761628	C₂×D₄	semidirect
230. #11761627	C₂×D₄	semidirect
235. Q₈×D₆₇	C₂×D₄	semidirect
267. D₄×D₆₇	C₂×D₄	semidirect
273. C₂×C₄×D₆₇	C₂×D₄	semidirect
304. #41×C₆₇	C₂×D₄	semidirect
343. Q₈×C₆₇	C₂²×D₄	semidirect
349. D₄×C₆₇	C₂²×D₄	semidirect
352. C₂×C₄×C₆₇	C₂²×D₄	semidirect
364. C₂²⋊D₆₇	C₂²×D₄	semidirect
367. C₂×Dic₆₇	C₂²×D₄	semidirect
378. D₂₆₈	C₂²×D₄	semidirect
387. C₄×D₆₇	C₂²×D₄	semidirect
388. C₄×D₆₇	C₂²×D₄	semidirect
389. C₄×D₆₇	H(5,𝔽₂)	semidirect
392. Dic₁₃₄	C₂²×D₄	semidirect
413. C₄×C₆₇	C₂×H(5,𝔽₂)	semidirect
418. Dic₆₇	C₂×H(5,𝔽₂)	semidirect
426. D₆₇	#3498	direct (N × H)
435. #3498	D₆₇	direct (N × H)
442. C₆₇	C₂×#3498	semidirect
449. C₂×H(5,𝔽₂)	C₂×D₆₇	semidirect
461. #550	C₂×D₆₇	semidirect
470. D₄²	C₂×D₆₇	semidirect
478. #535	C₂×D₆₇	semidirect
486. #532	C₂×D₆₇	semidirect
497. C₂×#127	C₂×D₆₇	semidirect
507. C₄×#41	C₂×D₆₇	semidirect
535. C₂×#41	C₂²×D₆₇	semidirect
536. C₂×#41	C₂²×D₆₇	semidirect
561. C₂²×D₄	C₂²×D₆₇	semidirect
562. C₂²×D₄	C₂²×D₆₇	semidirect
563. C₂²×D₄	C₂²×D₆₇	semidirect
570. C₄⋊Q₈	C₂²×D₆₇	semidirect
581. #127	C₂²×D₆₇	semidirect
582. #127	C₂²×D₆₇	semidirect
583. #127	C₂²×D₆₇	semidirect
588. #124	C₂²×D₆₇	semidirect
599. #121	C₂²×D₆₇	semidirect
600. #121	C₂²×D₆₇	semidirect
606. #120	C₂²×D₆₇	semidirect
610. C₄×Q₈	C₂²×D₆₇	semidirect
621. C₄×D₄	C₂²×D₆₇	semidirect
622. C₄×D₄	C₂²×D₆₇	semidirect
627. #117	C₂²×D₆₇	semidirect
640. C₂×C₄²	C₂²×D₆₇	semidirect
661. #41	D₄×D₆₇	semidirect
773. Q₈	C₂×D₄×D₆₇	semidirect
792. D₄	C₂×D₄×D₆₇	semidirect
814. C₂×C₄	C₂×D₄×D₆₇	semidirect
845. C₄	H(5,𝔽₂)×D₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×H(5,𝔽₂)×D₆₇	2
#22573987	2
#22573986	2
#22573985	2
#22573984	2
#22573983	2
#22573982	2
#22573981	2
#550×D₆₇	2
D₄²×D₆₇	2
#535×D₆₇	2
#532×D₆₇	2
C₂×#127×D₆₇	2
C₄×#41×D₆₇	2
C₆₇×#3498	2
C₂×#3498	67

Subgroups — #3498×D67 #31764146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3498×D₆₇ #31764146